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Author: J.M. Aarts
Publisher: Elsevier
ISBN: 0080887619
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces.The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned.With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems.
Author: Vijay Srinivasan
Publisher: CRC Press
ISBN: 0824756991
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Presents a theory of dimensioning synthesized from several areas of geometry, starting from the works of Euclid and culminating in some recent results in classification of continuous symmetry groups. Features numerous examples and illustrations for better understanding of concepts.
Author: Michael G. Charalambous
Publisher: Springer Nature
ISBN: 3030222322
Category : Mathematics
Languages : en
Pages : 262
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Book Description
This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case. Its distinctive feature is the emphasis on the negative results for more general spaces, presenting a readable account of numerous counterexamples to well-known conjectures that have not been discussed in existing books. Moreover, it includes three new general methods for constructing spaces: Mrowka's psi-spaces, van Douwen's technique of assigning limit points to carefully selected sequences, and Fedorchuk's method of resolutions. Accessible to readers familiar with the standard facts of general topology, the book is written in a reader-friendly style suitable for self-study. It contains enough material for one or more graduate courses in dimension theory and/or general topology. More than half of the contents do not appear in existing books, making it also a good reference for libraries and researchers.
Author: Yakov B. Pesin
Publisher: University of Chicago Press
ISBN: 0226662233
Category : Mathematics
Languages : en
Pages : 633
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Book Description
The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
Author: Jun-Iti Nagata
Publisher: Elsevier
ISBN: 1483275027
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Bibliotheca Mathematica, Volume 6: Modern Dimension Theory provides a brief account of dimension theory as it has been developed since 1941, including the principal results of the classical theory for separable metric spaces. This book discusses the decomposition theorem, Baire's zero-dimensional spaces, dimension of separable metric spaces, and characterization of dimension by a sequence of coverings. The imbedding of countable-dimensional spaces, sum theorem for strong inductive dimension, and cohomology group of a topological space are also elaborated. This text likewise covers the uniformly zero-dimensional mappings, theorems in euclidean space, transfinite inductive dimension, and dimension of non-metrizable spaces. This volume is recommended to students and specialists researching on dimension theory.
Author: C. Nastasescu
Publisher: Springer Science & Business Media
ISBN: 9789027724618
Category : Mathematics
Languages : en
Pages : 382
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Book Description
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of s9phistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Author: J.M. Aarts
Publisher: Elsevier
ISBN: 0080887619
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces.The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned.With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems.
Author: Fortunato Hernández
Publisher:
ISBN:
Category : Cosmology
Languages : en
Pages : 128
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Book Description
Author: Elizabeth D. Hutchison
Publisher: SAGE
ISBN: 1412941253
Category : Education
Languages : en
Pages : 657
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Book Description
What is it about the multiple dimensions of person, environment, and time that social workers need to understand? How do diversity and inequality play a role in human behavior? How does our biology, spirituality, and psychology impact behavior? And finally, what can we learn about how social institutions, families, groups, organizations and communities impact the vast range of human behaviors? The Third Edition of this powerful text aims to examine these dimensions by expanding on these important questions. In this text, you will meet social workers and clients from a variety of work settings and situations who bring the passion and power of social work to life through engaging case studies found throughout the text. These case studies help apply the latest theory and research to real life practice situations. The Third Edition offers new case studies and is thoroughly updated and revised to reflect recent census data, developing trends, and cutting-edge research on human behavior. New to the Third Edition: ? Added coverage of international issues: Human behavior is put in global context throughout the book. Increased focus on social justice and diversity: More content has been added on human diversity related to gender, race and ethnicity, culture, sexual orientation, and disability. Engages the reader through a variety of illustrative features: New case studies, exhibits, photos throughout, and Web resources have been added to provide the most up-to-date information.High-Quality Ancillaries!? Student Study Website: Help your students succeed with this new companion student study site at http: //www.sagepub.com/pandestudy/. Students can review chapter highlights and summaries, take practice quizzes, and study via student flash cards on the Web. In addition, students can download podcasts which contain important highlights presented by the author.'? Expanded Instructor?'s Resource CD: New to this edition, instructors can create tests using a new electronic test bank. In addition, this resource cd contains powerpoint slides, teaching tips, suggested classroom activities and more and is available to qualified adopters. IRCDs are available for qualified instructors only. To request an IRCD for this book please contact Customer Care at 1.800.818.7243 (6 am ? 5 pm Pacific Time) or by emailing
[email protected] with course name and enrollment and your university mailing address to expedite the process.Intended Audience? This text was developed for advanced undergraduate and graduate courses on Human Behavior in the Social Environment in departments of social work and psychology. Together with its companion volume, Dimensions of Human Behavior: The Changing Life Course (ISBN: 978-1-4129-4126-6), students will receive the most comprehensive coverage available on Human Behavior. The two volumes are also available at a discounted price as a bundle (ISBN: 978-1-4129-4128-0).
Author: Afaf Ibrahim Meleis
Publisher: Lippincott Williams & Wilkins
ISBN: 9780781736732
Category : Medical
Languages : en
Pages : 840
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Book Description
This text guides you through the evolution of nursing's theoretical foundations and examines the ways in which these principles influence the practice of the discipline."--Jacket.
Author: David Plunkett
Publisher: Oxford University Press
ISBN: 0190640413
Category : Law
Languages : en
Pages : 465
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Book Description
Understood one way, the branch of contemporary philosophical ethics that goes by the label "metaethics" concerns certain second-order questions about ethics-questions not in ethics, but rather ones about our thought and talk about ethics, and how the ethical facts (insofar as there are any) fit into reality. Analogously, the branch of contemporary philosophy of law that is often called "general jurisprudence" deals with certain second order questions about law- questions not in the law, but rather ones about our thought and talk about the law, and how legal facts (insofar as there are any) fit into reality. Put more roughly (and using an alternative spatial metaphor), metaethics concerns a range of foundational questions about ethics, whereas general jurisprudence concerns analogous questions about law. As these characterizations suggest, the two sub-disciplines have much in common, and could be thought to run parallel to each other. Yet, the connections between the two are currently mostly ignored by philosophers, or at least under-scrutinized. The new essays collected in this book are aimed at changing this state of affairs. Dimensions of Normativity collects together works by metaethicists and legal philosophers that address a number of issues that are of common interest, with the goal of accomplishing a new rapprochement between the two sub-disciplines.
